Personal torsion weapons
= Introduction = There is another long lasting disagreement about general mode of operation of some torsion-powered ballistas. This disagreement was sparked by Pseudo-Heron's cheiroballistra text after Marsden (1971) had interpreted it as a description of a relatively small and novel piece of artillery. Later the Xanten manuballista which was older, Vitruvian type (***reference***) shifted the discussion to whether personal torsion weapons existed in general. Regardless, the controversy around the cheiroballistra is most interesting and will be emphasized here. Some scholars (e.g. Marsden, Wilkins) have assumed the cheiroballistra was cocked with a winch. Then there are those (e.g. Baatz, Iriarte, Stevenson) who believe the cheiroballistra was cocked similarly to gastraphetes by pushing the slider back with one's bodyweight alone. It should be noted that Marsden did not have a chance to see any archaelogical remains of cheiroballistra -style ballistas before his early death. Therefore his views should not be overemphasized, even though he probably studied ancient artillery in more detail than anyone else before or after him. = Arguments against personal torsion weapons = Wilkins (1995) has lots of arguments in favor of a winched cheiroballistra in both of his JRMES articles (1995; 2000). First, he states that the cheiroballistra had the same spring diameter as old wooden-framed one-cubit or two-span ballistas and thus had to be cocked with a winch (1995: 39; 2000: 96). However, as Iriarte (2000: 57) points out, both Wilkins (1995: 21) and Marsden (1971: 223-224) increased the inner diameter of the washers given in text (2 dactyls minus washer rim thickness twice). This quickly led both into problems, the most immediate one being the inadequate length of the levers resting on top of the washers. If the spring diameter is enlarged, the levers - in text 3 dactyls long - would no longer protrude from the washers enough and tightening the spring bundles with a spanner would be impossible. Therefore Wilkins (1995: 24) had to lengthen the levers to 3,5d. Marsden (1971: 222) with his more conservative increase of washer diameter did not strictly have to do that - end result being that his levers did not protude from the washers and thus could not be used for rotating the washer with the tightening lever. Second, Wilkins (1995: 39; 2000: 94) clearly assumes all pre-cheiroballistra ballistas had winches. This idea is almost entirely based on two statements given by Heron in his Belopoeica (e.g. Marsden 1971: 21, 25). However, as is clear from Marsden's translations Heron is simply describing what the engineers had to do to be able create even stronger ballistas. No amount of text analysis will ever make Heron say that less powerful ballistas cocked in gastraphetes-style (Marsden 1971: 23) were discontinued or that torsion springs themselves - whatever their size - were too powerful to be cocked manually. It is clear that Wilkins places way too much faith in his interpretation of the statements made by an ancient author he considers authoritative (Wilkins 2000: 94, 99). Another argument in favor of a winched cheiroballistra is it's weight, as Wilkins (1995: 39) points out. The machine can't be too heavy, or the advantages of winchless operation are lost. Another related issue is the centre of gravity of the machine. According to Wilkins Digby Stevenson has reconstructed a gastraphetes-style cheiroballistra which weighed ~12 kilograms (Wilkins 1995: 39; 2000: 97). Iriarte's reconstruction weighs only 9 kilograms (Iriarte 2000: 65). Most of the weight of the machine comes from the metal parts - or parts thought to be made of metal. As many dimensions of these parts are missing, reconstructions will be highly subjective and will be based on the assumed strain levels the machine. Therefore the weight of winched cheiroballistras cannot be taken as proof against the stomach bow theory. Wilkins also argues - not very convincingly - that because the material for the handle (part of the triggering mechanism at the end of the slider) was said to be of iron, it should be taken as a further proof that cheiroballistra was winched (Wilkins 1995: 16). He argues that usually P.H. did not state which material to use, so unless considerable strain was placed on the handle, other material such as bronze should have been perfectly satisfactory and no mention of iron would have been necessary. This does not make much sense to me, as the material for the little ladder and it's rungs and cross-piece are not given, either, and these are under considerable stress, too (see Marsden 1971: 214-217; Wilkins 1995: 27-28). Also, the weakest link in the handle and slider construction is the wooden slider, not the handle. This is because the handle is attached to the end of the slider and - as we know - wood splits very easily. Wilkins (1995: 16) noticed this and realized that the end of the slider had to be reinforced with metal plating. Finally, as Iriarte (2000: 57) points out, there is archaeological evidence of small ~2 dactyl washers from Ephyra and Elginhaugh. This proves that small ballistas were in fact used. There are basically two ways to discredit these finds. First, one can argue that this kind of small washers were never used widely and these are just isolated cases. This is, however, unlikely due to how archaeological record is formed. Archaeological finds consist almost exclusively of abandoned and/or lost items. In addition, only a small fraction of the items that were lost or abandoned ever reach the archaeological record for a variety of reasons. So, unless were talking of a closed find such as a city overrun by volcanic ashes or covered by a landslide - or perhaps a shipwreck - we're most likely going to encounter common items of little monetary or reuse value. This means it's likely that small washers were common, not rare, and we're going to find lots of them in the future. The second counterargument is that the washers belonged to "toys", not real weapons. Whether they were toys did not depend on the washer diameter but the performance (as defined here) of the ballistas they belonged to. In a nutshell there is no reason to forcefully interpret the cheiroballistra text to describe a winched weapon or to try discrediting the stomach-bow theory as Wilkins (1995: 38-41; 2000: 94-100) does. = Power vs. performance = I found it necessary to write this section because Wilkins seems to consistently confuse power with performance. Here power refers to either power fed into the system (ballista) or the kinetic energy of the projectile. Performance, on the other hand, refers to the weapon's usability and effectiveness in conflict situations (sieges, battlefield etc.). Wilkins (2000: 94, 96) argues that cheiroballistra stomach-bow proponents are not taking into account the "performance requirements" of ancient catapults. Being a winch proponents what he really meant to say is "power requirements". He does not take into account the performance of the weapon as defined here. What is clear, however, is that the cheiroballistra had to be somehow superior to handbows and other missile weapons of the era to make any sense. Unlike Wilkins seems to think, power is only small part of the equation. Other factors include things like cost of manufacture, ammunition and training, as well as power, accuracy, range, initial velocity and weight of ammunition. One key factor is also the efficiency of energy transfer, meaning how much of the energy put into the torsion springs is transmitted into the bolt as kinetic energy. Being superior to contemporary missile weapons even in one or few of these areas might be enough to justify use of relatively low-powered hand-cocked weapon. Cheiroballistra's only undisputed disadvantages compared to the handbow is it's weight and somewhat slower rate of fire. Cost might be another, but complex handbows made from sinew, wood and horn were not cheap, either. Also, unlike Wilkins (2000: 96) thinks, the weight of the ballista bolt has little to do with it's performance as a weapon. He argues that light bolts (as in 25 or 42 grams) would be useless in war. This is the case only if the bolt's speed is very low similarly to those in Wilkins' own reconstructions (Wilkins 2000: 93): * Winched cheiroballistra: 47m/s with 100 gram bolt (110 joules). Apparently the pull was around 739 pounds as in Wilkins' earlier tests. Power stroke was apparently around 60 cm. * Winched three-span ballista: 37m/s with 200 gram bolt (136 joules). Power stroke length unknown. As a comparison a few tests from the author and from Tim Baker who has done extensive research on performance of traditional handbows: * From Baker (2000: 114-115), all bows drawn 71.12 cm (28"): ** Average 40 lbs all-wood, straight handbow: 42,09 m/s avg using a 32,5 gram arrow (29 joules) ** Average 50 lbs all-wood, straight handbow: 45,75 m/s avg using a 32,5 gram arrow (34 joules) ** Average 60 lbs all-wood, straight handbow: 49,72 m/s avg using a 32,5 gram arrow (40 joules) ** Average 70 lbs all-wood, straight handbow: 53,99 m/s avg using a 32,5 gram arrow (47 joules) * Author's ~150 lbs crossbow with steel bow, power stroke 33,5 cm: ** 55,7 m/s avg using a 28 gram bolt (44 joules) ** 47,7 m/s avg using a 50 gram bolt (56 joules) * Author's ~300 lbs crossbow with steel bow, power stroke 27,5 cm: ** 60,6 m/s avg using a 47 gram bolt (86 joules) ** 49,4 m/s avg using a 81 gram bolt (99 joules) Perhaps as important as the energy output of a given bow, crossbow or a ballista is it's efficiency of energy transfer. This can be calculated by plotting it's force-draw curve as described here and comparing the stored energy to the velocity of the projectile. A well-made bow or crossbow will convert about 70% of it's stored energy into the projectile's kinetic energy, provided the projectile is heavy enough. As the force-draw curve of an outswinger is very close to that of a normal bow, we can roughly calculate the efficiency of Wilkins cheiroballistra, which has a force-draw curve pretty similar to this: The area below the curve represents the stored energy, which in this case (739 pounds at 60cm) is roughly 745 joules. Given the projectile has 110 joules of energy, efficiency of the cheiroballistra is mere 14,7%. This means that four times as much time has to be spent cranking the ballista than if it was working at normal efficiency levels. As a weapon of war Wilkins' cheiroballistra would have been useless due to their weight, slow rate of fire and poor range. And efficient version of the same winched cheiroballistra should output at least 50% of the input energy, or 373 joules, which would give the same bolt a velocity of 86 m/s. In practice, the velocity could be significantly higher or lower, depending on a number of factors. = Performance of a personal torsion weapon = Unlike Wilkins thinks, light bolts from a properly designed ballista would have been effective, as long as the velocity was high enough. There is evidence that a properly designed Orsova ballista reconstruction with inswinging arms can consistently reach velocities of 300fps (90 m/s) with ~400 gram ammunition and 5000 pound draw weight. As of 20th August 2010 this Orsova reconstruction has not yet even reached it full potential (drawn only ~90 degrees) but still it shoots bolts at almost double velocity compared to Wilkins' reconstruction. This velocity increase alone would amount to 4x increase in kinetic energy. In addition, the same engine is has had well-documented 400fps+ (~120m/s) shots. There is no reason to think that velocity would be significantly reduced by scaling down the machine, as long as bolt weight is scaled down, too. According to Wilkins (2000: 97), the average stomach pressure of a man is around 68 kg. If we simplify slightly, this means that at no point can the force-draw curve of the cheiroballistra rise above 68kg, or cocking it won't be possible (for an average man). We can estimate the form of the force-draw curve of an inswinger relatively easily, if we assume that each degree of rotation feeds (roughly) the same amount of energy into the torsion springs. This can be done using the simple geometric calculations explained here. This gives us a estimate of the force-draw curve - and energy storage capability - of an inswinging cheiroballistra with maximum draw weight of 68kg: Notice the flatness of the force-draw curve for an inswinger: it means that a great deal more energy can be stored than in an outswinger without tripping over the maximum draw weight limit (68kg). Interestingly, it would make sense to stop rotating the arms slightly earlier, at around 150 degrees to avoid the sharp rise of draw weight at the end. This would allow the earlier part of the curve to be higher, thus increasing stored energy considerably, as in the optimized curve above. That said, the maximum draw weight depends greatly on the cocking technique: it may be that the optimized cheiroballistra would be very difficult to cock effectively, even if it's final draw weight was kept lower than in the "normal" one. According to these force-draw curve calculations the inswinging cheiroballistra can store roughly 160 joules of energy, whereas an outswinger would only store ~120 joules, depending on the concavity of it's F/D curve, or in archery terms, the final bowstring angle. The optimized inswinger version with 150 degree arm rotation would store around above 300 joules of energy. If we estimate 70% efficiency, we get energy output of 112 joules for the inswinger and 84 joules for the outswinger. Efficiency of energy transfer, or dynamic efficiency depends on projectile weight, among other things. Unfortunately the F/D curve tells us nothing about that. Assuming standard 70% efficiency, we get the following projectile velocities at given bolt weights: Based on Nick Watt's Orsova reconstruction bolts weights of 15-35 grams are most likely, with velocities of 80-122m/s. Even 80m/s would have given the cheiroballistra clear edge on range when compared to handbows. However, only real reconstruction that uses sinew for torsion springs can tell what the cheiroballistra was capable of. Many scholars have used archaeological finds of bolts or boltsheads as basis for their ballista missile (e.g. Iriarte 2000: 66-68; Wilkins 1995: 45; Wilkins 2000: 95-96). This is dangerous because it tends to limit testing to random bolts originally belonging to random ballistas (or even crossbows). This almost certainly gives false impression of a ballista's capabilities such as range and power. The problem should approached the other way around, by rigorously testing different bolt weights to find the best match between kinetic energy and initial velocity for each individual ballista. If too light bolt is used, the arms have lots of energy left at the end. On the other hand, if too heavy bolt is used, the ballista will transfer energy efficiently into the bolt, but the initial velocity and range of the bolt may be disappointing. Category:Historical research Category:Archaeological research Category:Physics Category:Backup Category:Two-armed torsion engines Category:Theoretical